A GIS tool for spatiotemporal modeling under a knowledge synthesis framework

Abstract

In recent years, there has been a fast growing interest in the space–time data processing capacity of Geographic Information Systems (GIS). In this paper we present a new GIS-based tool for advanced geostatistical analysis of space–time data; it combines stochastic analysis, prediction, and GIS visualization technology. The proposed toolbox is based on the Bayesian Maximum Entropy theory that formulates its approach under a mature knowledge synthesis framework. We exhibit the toolbox features and use it for particulate matter spatiotemporal mapping in Taipei, in a proof-of-concept study where the serious preferential sampling issue is present. The proposed toolbox enables tight coupling of advanced spatiotemporal analysis functions with a GIS environment, i.e. QGIS. As a result, our contribution leads to a more seamless interaction between spatiotemporal analysis tools and GIS built-in functions; and utterly enhances the functionality of GIS software as a comprehensive knowledge processing and dissemination platform.

where g is a vector of g-functions (α = 1, 2,…) that represents stochastically the G-KB under consideration (the bar denotes statistical expectation). In Eq. (1), μ is a vector of μα-coefficients that depends on the space–time coordinates and is associated with g. Specifically, the μα express the relative significance of each g-function in the composite solution sought. The maximum entropy principle is employed to enable incorporation of as many relevant G-KB sources available in an initial prior stage. Mathematically, it formulates the prior probability density function (PDF) \( e^{{u^{T} g}} \) that is constrained by the G-KB, as shown in the first equation of Eq. (1). The second equation of Eq. (A1) represents succinctly the second stage in BME analysis, known as posterior of integration stage, where \( \zeta_{s} \) represents the S-KB available, and A is a normalization parameter. The integration stage uses operational Bayesian updating theory (Christakos 2002) to conditionalize the site-specific S-KB on the prior G-KB. By doing so, it effectively blends all available information about our attribute to produce posterior PDFs, designated as fK, across all space and time locations we seek results. The g and \( \zeta_{s} \) are the inputs in Eq. (1), whereas the unknown are the μ and fK across space–time.

References

Akita Y, Serre M (2009) BMEGUI user manual. Department of Environmental Sciences and Enginnering, School of Public Health, University of North CarolinaGoogle Scholar